Debye temperature table

Table A6.7 summarizes the thermodynamic properties of monatomic solids as calculated by the Debye model. The values are expressed in terms of Bq/T, where 6q is the Debye temperature. Tables A6.5 to A6.7 are adapted from K. S. Pitzer, Thermodynamics, McGraw-Hill, New York, 1995.

A detailed study of the electrical resistivity behavior of the La272ln and Ce272ln (T = Ni, Cu, Rh, Pd, Pt, Au) indides was performed by Kaczorowski et al. (1996a, 1996b). They evaluated the electrical resistivity data according to the modified Bloch-Griineisen relation and derived the Debye temperatures (table 17). 

Fig. 33.7 Disparity of the 6>dx and die tjx (R is the gas constant) of the segmented H-bond gives rise to the complex specific heat curve exhibiting four temperature regions. The number of regions coincides with that demonstrated by the p(T) profiles [25, 41, 42]. Because of the difference in their Debye temperatures (Table 33.1), the specific heat i/l of the 0 H rises faster toward the asymptotic maximum value than the i/h- The four regions correspond, respectively, to the phases of liquid (I), solid (HI, IV), and liquid-solid transition (II) with different specific heat ratios. At extremely low temperatures (IV), i/l i/h 0. (The t/j. in the solid phase differs from the in the liquid, which does not influence the validity of the hypothesis.) The crossing points correspond to the density extremes (Reprinted with permission from [14])...

Table 3 Room-temperature elastic constants, density, and the Debye temperature p of a number of Pd-Ni-P and Pd-Cu-P bulk amorphous alloys. The elastic moduli are in units of GPa and the density p is in units of g/cm. ...

The calculated Debye temperatures are also listed in Table 3. From this table, it is clear that the elastic properties of the bulk amorphous Pd-Ni-P and Pd-Cu-P alloys change little with changing composition. The elastic moduli of the Pd-Cu-P alloys are slightly lower than those for the Pd-Ni-P alloys. 

Table 7.8 Summary of results obtained for the four Os Mossbauer transitions studied. The absorber thickness d refers to the amount of the resonant isotope per unit area. The estimates of the effective absorber thickness t are based on Debye-Waller factors / for an assumed Debye temperature of 0 = 400 K. For comparison with the full experimental line widths at half maximum, Texp, we give the minimum observable width = 2 S/t as calculated from lifetime data.

Ld = 1/A is the Debye length Table 3.1 shows values for several concentrations of a 1-1 electrolyte in an aqueous solution at room temperature. The solution compatible with the boundary condition oo) = 0 has the form 4>(x) = Aexp(—kx), where the constant A is fixed by the charge balance condition ... 

Table 8.2. Debye temperature ( p in K) and electronic heat capacity coefficient (see Section 8.4) (yin mJ K-1 mol-1) of the elements.

Table 8.3 Comparison of Debye temperatures derived from heat capacity data and from elastic properties.

Even better agreement is observed between calorimetric and elastic Debye temperatures. The Debye temperature is based on a continuum model for long wavelengths, and hence the discrete nature of the atoms is neglected. The wave velocity is constant and the Debye temperature can be expressed through the average speed of sound in longitudinal and transverse directions (parallel and normal to the wave vector). Calorimetric and elastic Debye temperatures are compared in Table 8.3 for some selected elements and compounds. 

Vibrations in the surface plane, however, will be rather similar to those in the bulk because the coordination in this plane is complete, at least for fee (111) and (100), hep (001) and bcc (110) surfaces. Thus the Debye temperature of a surface is lower than that of the bulk, because the perpendicular lattice vibrations are softer at the surface. A rule of thumb is that the surface Debye temperature varies between about 1/3 and 2/3 of the bulk value (see Table A.2). Also included in this table is the displacement ratio, the ratio of the mean squared displacements of surface and bulk atoms due to the lattice vibrations [1]. 

Table A.2 Ratio of surface and bulk displacements, and Debye temperatures of several metals f 1],...

Table 3.1 Entropy values obtained by application of Einstein (E), Debye (D), and Kieifer (K) models, compared with experimental data at three diiferent temperatures. Data are expressed in J/(mole X K). Values in parentheses are Debye temperatures (d, ) and Einstein temperatures (9 ) adopted in the respective models (from Kieifer, 1985).

Crystal engineering synthons Table 1.5. Debye temperatures of selected MOMs... 

Table 1 Debye temperatures for some elemental solids and simple compounds. Data are obtained from thermal measurements at low temperature [25]...

Table 4.8 Representative Values of Debye Temperature for Selected Elements...

Table B.l lists all the chemical reactions and their temperature dependence. Table B.2 lists the Debye-Hiickel constants A,p and Av) as a function of temperature and pressure. Table B.3 lists the numerical arrays used for calculating unsymmetrical interactions (Equations 2.62 and 2.66). Table B.4 lists binary Pitzer-equation parameters for cations and anions as a function of temperature. Table B.5 lists ternary Pitzer-equation parameters for cations and anions as a function of temperature. Table B.6 lists binary and ternary Pitzer-equation parameters for soluble gases as a function of temperature. Table B.7 lists equations used to estimate the molar volume of liquid water and water ice as a function of temperature at 1.01 bar pressure and their compressibilities. Table B.8 lists equations for the molar volume and the compressibilities of soluble ions and gases as a function of temperature. Table B.9 lists the molar volumes of solid phases. Table B.10 lists volumetric Pitzer-equation parameters for ion interactions as a function of temperature. Table B.ll lists pressure-dependent coefficients for volumetric Pitzer-equation parameters. Table B.12 lists parameters used to estimate gas fugacities using the Duan et al. (1992b) model.

Heat capacity is (9.1 + 2.9 x 10 3 T(K)) cal mol 1 K 1 between 298 and 1273 K, while entropy is 10.4 cal mol 1 K 1 at 298.15 K [30], More recent heat capacity data between 153 and 293 K are quoted in TABLE 3, Datareview A1.4 of this volume. There is a 7.5% discrepancy between the two sets of data at room temperature. The inferred Debye temperature is 660 K [29], Enthalpies, entropies and Gibbs functions of fusion and formation are given in TABLE 4. Thermochemical data should also be regarded with circumspection in particular the early value of AH°f = -5 kcal mol 1 [1] is often quoted but should now be discarded in favour of more recent results [24,31] found to lie close to those for the other nitrides. 

The relations between experimental quantities mostly concern the temperature effects. First, let us consider the specific heat. In Chap. XV, Sec. 3, we have seen that it should be fairly accurate to use a Debye curve for the specific heat of an alkali halide, using the total number of ions in determining the number of characteristic frequencies in that theory. It is, in fact, found that the experimental values fit Debye curves accurately enough so that we shall not reproduce them. We can then determine the Debye temperatures from experiment, and in Table XXIII-5 we give these values for NaCl and KC1, the two alkali halides... 

Table XXIII-5.—Debye Temperatures for Alkali Halides...

XIV, wc have information from which the Debye temperature can be calculated from the elastic constants and the density. These constants are known for NaCl and KC1, and in the table we also give the calculated Debye temperature found from the elastic constants. Finally, in Chap. 

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